A block is partially immersed in a liquid and the vessel is accelerating upwards with an acceleration $"a".$ The block is observed by two observers ${\mathrm{O}}_1$ and $O_{\mathit{2}}\mathit{,}$ one at rest and the other accelerating with an acceleration $"a"$ upward. The total buoyant force on the block is :

The cubical container $\mathrm{ABCDEFGH}$ which is completely filled with an ideal (nonviscous and incompressible) fluid, moves in a gravity free space with $a$ acceleration of $a=a_0\left(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}\right)$, where $a_0$ is a positive constant. Then the pressure will be minimum at point 

One end of a long iron chain of linear mass density $\lambda$ is fixed to a sphere of mass m and specific density $1/3$ while the other end is free. The sphere along with the chain is immersed in a deep lake. If specific density of iron is $7$, the height $h$ above the bed of the lake at which the sphere will float in equilibrium is (Assume that the part of the chain lying on the bottom of the lake exerts negligible force on the upper part of the chain.)

Equal volumes of a liquid are poured in the three vessels $A, B$ and $C\left(h_1<h_2<h_3\right).$ All the vessels have the same base area. Select the correct alternatives.